Strain-softening Characteristics Research Articles

Experimental Investigation on the Shear Characteristics of Frozen Silty Clay and Grey Relational Analysis

In the spring thawing season, the decrease in the strength of frozen soil caused by temperature may lead to slope instability. Therefore, researchers have studied the relationship between the temperature and strength of the freeze-thaw zone. However, previous studies have considered the impact of thawing temperature on the strength, but less research on shaping temperature. Therefore, direct shear tests were performed on specimens with different thawing temperatures (i.e., −5, −2 and 1 °C) and different water contents (i.e., 9, 16, and 23%) at different shaping temperatures (i.e., −2, −7 and −12 °C). The results indicated that: the stress-strain curves under different test conditions exhibited strain softening characteristics; shear strength and shear index decreased with increasing shaping temperature; the effect of cohesion on strength was greater than that of internal friction angle; the mechanical mechanism in the freeze-thaw zone was related to the unfrozen water content of the specimen. In addition, the grey correlation analysis showed that the water content had the greatest effect on the shear index, while the shaping temperature had the least effect on the shear index. The grey relational grade of shaping temperature was greater than 0.5, indicating that the effect of shaping temperature on strength was not negligible.

Estimation of the detection distances of CPT resistance

Cone penetration test (CPT), a common method for engineering geological exploration, is often used for empirical delineation of soil stratigraphy, but its accuracy mainly depends on the engineers' judgment of the detection distances of CPT resistance in the multi-layer soil. The detection distances, the distance from the cone tip to the soil interface when the resistance trend changes, were studied in this work. Firstly, a theoretical solution of cone resistance was proposed, based on cavity expansion theory and the geometry of the probe. The solution divided the disturbed soil around the probe into three regions, considering the strain-softening characteristics of soil. And an innovative assumption that the soil under the cone expands cylindrically with variable radius, was justified by the oval profile of soil particles in a series of transparent soil tests. Both theoretical results and test results illustrated that the detection distances of CPT resistance depended on the soil properties and the thickness of the interlayer. Compared with numerical results and literature data, the detection distances in the strong soil were greater than those in the weak soil of the two-layer soil, and the distances reduced as the strength difference of adjacent soil decreased. Besides, the thin-layer effect was investigated within the maximum thickness which was smaller in strong interlayer soil. When the maximum thickness was exceeded, the determination method for detection distances in two-layer soil could be applicable. The results contribute to the application of CPT in geologic investigation.

Study on Cyclic Bearing Capacity of Suction Pile Based on Equivalent Cyclic Creep Model

In the process of cyclic loading, strain development not only presents the strain softening phenomenon, but also a strain hardening phenomenon, depending on the different values of static deflection stress. The strain hardening and strain softening characteristics of soft clay are studied by cyclic triaxial tests. The test results show that when the static deflection stress is zero, the value of cyclic cumulative strain is small, and the strain development presents the softening phenomenon. When the static deflection stress is greater than zero, the accumulation strain increases with increasing cyclic deflection stress, and the strain development present strain hardening phenomenon. Therefore, a strain softening index and strain hardening index were proposed to describe the cyclic characteristics of soil. Moreover, an equivalent cyclic creep model was established by considering the strain hardening index to describe cyclic characteristics of suction pile. The results obtained using the proposed method are in reasonably good agreement with the measured results. This can provide a new method for analyzing the cyclic characteristics of soil and the suction pile.

Tensile properties of cement-stabilised clays and their contribution to seawall design

Deep cement mixing is a typical ground improvement technique, and has recently been introduced in some large-scale reclamation projects in Hong Kong. There is a lack of internationally recognised testing standard for determining the tensile strength of cement-stabilised soil. In this study, tensile properties of cement-stabilised clays have been investigated using direct tension test and Brazilian test. The interpretation of tensile strength in Brazilian test is not straightforward due to the formation of multiple cracks during loading. As such, focus is placed on the validation of the fundamental assumption on crack initiation mechanism. A consolidated database of tensile strengths of cement-stabilised soils is compiled. A constitutive model in the finite-element program Plaxis, namely concrete model, has been studied. This model, originally aiming to simulate the behaviour of concrete and shotcrete, duly considers the cracking and the strain-softening characteristics, and is able to reasonably simulate the fundamental tensile behaviour of cement-stabilised soil. Numerical simulations have been carried out using the concrete model to assess the stability of seawall founded on cement-stabilised clay. Tensile properties are found to have an important bearing in maintaining the stability of the seawall when column-pattern stabilisation is adopted.

Analysis of interface mechanical properties between geotextiles and tailings during pull-out tests.

Considering the strain-softening characteristics of the pull-out interface between geotextiles and tailings; to determine the interface interaction characteristics, this paper proposes a trilinear shear stress displacement softening model of geotextile-reinforced tailings. The obtained nonlinear governing equations were dimensionless, which were expressed in finite difference form. The results indicated that an accurate numerical solution could be obtained within a reasonable calculation time by discretizing the reinforcement length into 300 units. Three new dimensionless interaction terms, namely, the relative stiffness α, relative displacement β, and relative interface shear stiffness η of the reinforcement-tailings interaction, were introduced. In addition, an estimation method based on the approximate value of the relative stiffness α of the reinforcement-soil interface in the low-tensile-force displacement range was proposed. The interface shear stress range according to parameters α, β, and η was parameterized, and the normalization relationship between the tensile force and pull-out end displacement was determined. The numerical values calculated by the model were compared with the pull-out test results, demonstrating that the proposed model can accurately predict the pull-out behavior of the extensible reinforcement.

Strain rate effect of frozen ballast aggregates under compression: Experiments and discrete element simulations

Ballast railway tracks in cold regions are typically affected by severe freezing damage. To further investigate the mechanical properties of the ballast layer under freezing conditions, ice–bonded ballast specimens are prepared, and uniaxial compression tests are performed in a low-temperature environment. The effect of strain rate on the stress–strain curve, failure mode, and compressive strength are discussed comprehensively under two ice content ranges. Meanwhile, a dilated polyhedron discrete element method based on bonded particle model (DP-DEM-BPM) was developed to establish the discrete element model of ice–bonded ballast under uniaxial compression. The results show that the strain rate significantly affects the deformation characteristics of the frozen specimens. When the strain rate is low, the stress–strain curves exhibit clear strain-softening characteristics. As the strain rate increases, the post-peak stress decreases more rapidly, and the brittleness becomes more prominent. Meanwhile, the strain rate can be categorised into ductile, ductile–brittle transition, and brittle zones based on the stress–strain curve and failure mode. The specimens in the ductile zone primarily present axial splitting failure, whereas those in the brittle zone present brittle fracture with multistage local crushing. The corresponding discrete element simulation reveals the internal mechanism of failure modes in the specimen from the point of view of the bond. In addition, the uniaxial compressive strength and effective elasticity modulus increase in the ductile zone and then decrease in the brittle zone as the strain rate increases. The relationship between compressive strength and strain rate can be expressed using a piecewise function.

Improved peridynamic model and its application to crack propagation in rocks.

The conventional bond-based peridynamics (BB-PD) model is suitable for simulating the failure mode of homogeneous elastic-brittle materials. However, the strain hardening and subsequent strain softening characteristics of rocks under loading cannot be reflected. In addition, the fracture mechanisms of rock materials under tension and compression are completely different. To solve these problems, this paper proposes an improved BB-PD model using different fracture criteria in the tensile and compression stages of the bond based on previous improved models, and a critical failure condition obeying the Weibull distribution is introduced to reflect the heterogeneity of the rock. The crack propagation processes of an intact rock specimen, rock specimen with a single pre-existing flaw and rock specimens with two and three pre-existing flaws under compressive loading are simulated using the model, and its feasibility is verified by comparing with the results of previous laboratory tests. Next, the effects of the inclination angle and length on the wing crack propagation length are studied. Finally, the changes in the crack aggregation modes under different rock bridge inclination angles are simulated. Eight types of crack aggregation modes are found, and the conditions under which they may occur are analysed. The improved model proposed can effectively simulate the crack propagation and coalescing processes and has a wide application prospect for rock fracture simulations.

Numerical simulation of strain-softening behavior of glass-filled polymer composites: Comparison of two-dimensional and three-dimensional analyses using Arruda-Boyce and Three-Network viscoplastic models

Most polymers and stiff-filler reinforced polymer composites exhibit post-yield strain-softening characteristics under large deformation mechanical loading. Singh et al. [Polymer Composites, 40 (12), pp. 4726–4741, 2019] conducted compression tests on glass-filled epoxy composites, altering the shape and volume percent of the glass fillers, and observed a dominant strain-softening tendency immediately after the yield stress values. This study aims to capture the post-yield strain-softening characteristics of glass-filled epoxy composites reported by Singh et al. using finite element analysis (FEA). Arruda - Boyce (AB) and Three Network (TN) viscoplastic constitutive material models are used as matrix behavior to perform numerical simulations on two-dimensional and three-dimensional representative volume elements (RVEs), where spherical (circular in 2D) and milled/cylindrical (rectangular in 2D) fillers are randomly positioned and oriented inside. When the calibrated AB and TN models were used to simulate the stress-strain response of the pristine matrix, both models numerically converged and were in good agreement with the experimental results. However, when filler-reinforced polymer composites are considered, the simulations using the AB model become unstable and fail to converge soon after the yield stress (at small strain values) is reached. Whereas simulations using the TN model take a short period to converge to large strain values compared to the former model. The existence of an extra elastic-viscoplastic network in the TN model improves stability in the model's strain-softening zone, allowing for faster numerical convergence. Therefore, the TN model can be used to simulate the strain-softening behavior of both pristine and stiff-filler-reinforced polymer composites under large deformations. The true stress versus true strain data retrieved from the FEA of the two-dimensional and three-dimensional simulations using the TN model were compared with experimental data. When the TN constitutive model was used in three-dimensional simulations instead of the AB viscoplastic model, the elastic modulus, yield stress, and post-yield strain-softening characteristics of the spherical particle and milled fibre epoxy composites were shown to predict the experimental data rather well.

Study on Mechanical Properties and Nonlinear Strength Model of Deep Water-Sensitive Rock in Xianglu Mountain Tunnel

The complex mechanical properties of deep water-sensitive rocks during construction bring great challenges to the construction and stability analysis of underground engineering in water-sensitive strata. Taking Xianglu Mountain Tunnel in the Central Yunnan Water Diversion Project as the engineering background, the mechanical properties of two types of water-sensitive rocks including limestone and silty mudstone were studied through laboratory tests, and a nonlinear strength model based on Hoek-Brown criterion was proposed. The results show that (1) the stress-strain curves of deep limestone and silty mudstone have significant strain softening characteristics and brittle-ductile transformation trend. Compared with limestone, silty mudstone has stronger ductility and lower critical confining pressure for brittle-ductile transformation; (2) the dilation effect of rock is affected by both confining pressure and plastic deformation. Under the same confining pressure and plastic deformation, the dilation characteristic of limestone is more evident than that of silty mudstone; (3) the Hoek-Brown criterion can describe the nonlinear strength characteristics of deep rock well. The evolution law of strength parameters m b and s with modified plastic shear strain conforms to the negative exponential function, while the relationship between strength parameter a and modified plastic shear strain satisfies cubic polynomial function; (4) the simulation results based on the nonlinear strength model are consistent with the test results, and the established strength model has high reliability. The research results can provide a basis for the stability analysis of the Xianglu Mountain Tunnel and the optimal design of the supporting structure and can also provide a reference for the study of the mechanical characteristics of the deep rocks in water-sensitive strata.

Simulation and analysis of corrosion fracture of reinforced concrete based on phase field method

Reinforced concrete has been widely used. However, it is difficult to accurately simulate the process of concrete damage and destruction caused by rebar corrosion. Therefore, the objective of this work is to solve this difficult problem using a phase field method and analyze the failure process of reinforced concrete. The main importance of this work is to improve the calculation method for the problem, simulate the damage and destruction of concrete cover, and visualize the crack propagation process. Based on the strain softening characteristics of concrete the damage of concrete cover caused by uniform and non-uniform corrosion of rebars is simulated respectively. The simulation results are consistent with the actual observation. The applicability of the phase field method for complex crack propagation in reinforced concrete is verified, which provides a reference for the engineering design and durability research of structures. Analysis of simulation results found that the crack propagation speed is fast for uniform corrosion. Increasing the thickness of concrete cover is benefit to improve the corrosion resistance of structure. However, the crack propagation speed is slow for non-uniform corrosion. The thickness of the cover has no obvious effect on the corrosion damage resistance of structure. For the non-uniform corrosion of multiple rebars, depending on the thickness of concrete cover and the spacing between rebars, the concrete cover presents three typical crack propagation morphologies: wedge-shaped cracks, layered cracks and small local cracks.

Acoustic emission characteristics and energy mechanism of CFRP-jacketed coal specimens under uniaxial compression

Fiber-reinforced polymer (FRP) wrapping is a potentially attractive coal-pillar reinforcement technique. To study the effect of carbon fiber-reinforced polymer (CFRP) jacketing on mechanical properties, crack evolution, and energy dissipation mechanism of coal specimens, a series of uniaxial compression tests with acoustic emission (AE) monitoring were conducted on coal specimens with 0–2 CFRP-jacket layers. The results showed that the CFRP jacket had visible effects on the core failure process of coal specimens. (1) With an increase in the number of CFRP-jacketed layers, the specimens showed stronger strain-softening characteristics in the unstable crack growth stage, and the damage stress threshold increased significantly. (2) The correlation analysis between average frequency (AF) and rise angle (RA) demonstrated that with an increase in the number of CFRP-jacketed layers, the tendency of crack classification to change from tensile mode to shear mode increased. (3) The spatiotemporal evolution of AE event locations showed that CFRP jackets changed the AE event location concentration mode from a longitudinal distribution along the coal specimen to a distribution near the fracture. Moreover, the strain energy density evolution of coal specimens with 0–2 layers of CFRP jacketing was analyzed based on the mechanical equilibrium and energy conservation of CFRP-jacketed coal specimens. The dissipation strain energy ratio was introduced to define the damage variable, and the damage constitutive model with regards to CFRP jackets was constructed; the model describes the CFRP-jacketed coal specimen stress–strain relationship for strain-hardening, strain-softening, and sudden failure.

DEM simulation of geotextile-geomembrane interface direct shear test considering the interlocking and wearing processes

Geotextile-geomembrane interface has low shear strength and strain-softening characteristics which might induce progressive failure in landfills. The interlocking between asperities and filaments and wearing of them have significant influence on the interface shear behaviors between textured geomembrane (GMB) and thermally bonded nonwoven geotextile (TBNG), but the microscale mechanism has not been clearly revealed before. Using discrete element method (DEM), textured GMB with breakable asperities and TBNG made up of randomly distributed fibers are generated. The micromechanical parameters of the two materials and the interface are calibrated using existing experimental data. Parametrical study about asperity bonding level, inter-fiber bonding level and inter-particle frictional coefficient are conducted to quantitatively investigate the interlocking behavior on the scale of asperities and filaments. The asperity bonding level greatly affects the interlocking effect between asperities and geotextile matrix and plays a dominant role in shear mode (frictional behavior and interlocking behavior). The influence of inter-fiber bonding level on the interface shear behavior is significant for textured GMB with strong asperities and is negligible for smooth GMB. The shear strength and post-peak reduction level are enhanced with larger inter-particle frictional coefficient. The present study provides an applicable tool to investigate the microscale mechanical behaviors of TBNG-GMB interface.

Pullout Characteristics and Damage Softening Model of the Geogrid-Soil Interface

The mechanical properties of geogrid-soil interface is very important in design and stability analysis of reinforced soil structure. In order to study the complicated mechanism of geogrid-soil interface, a series of pullout tests of HDPE uniaxial tensile geogrids with the different transverse ribs spacing is used to investigate the interaction characteristics in the laboratory. The test results show that pullout force and displacement curves are characterized as strain softening; compared with the no-reinforced case, the case reinforced with geogrid has larger cohesion and lower friction angles. The ductility of soil is enhanced due to geogrid reinforcement. Based on the basic control equations of the interface and damage theory, trilinear shear stress-displacement damage softening model is proposed to describe the strain-softening characteristics of geogrid-soil interface. Analytical solutions of interface tension, shear stress, and displacement at different stages are derived considering strain softening based on damage, and the development of shear stress and progressive failure mode of the geogrid-soil interface at different pullout stages is revealed. Furthermore, the proposed model is verified by experimental results.

Analysis of Failure Behavior Based on the Ring Shear Test in a Bedding Rock Landslide of the Three Gorges Reservoir

Complex geological environment and climatic conditions lead to frequent geological disasters in the Three Gorges Reservoir area. In particular, due to the impact of reservoir impoundment, a large number of landslides have occurred, resulting in huge economic losses and casualties. In this study, the bedding rock landslide is taken as the research object. First, the DTA-138 geotechnical ring shear apparatus system is used for the ring shear test. Second, a two-dimensional numerical model of Shanshucao landslide was established, and simulation was carried out. The main conclusions are as follows: 1) The shear stress–shear displacement curves of sliding zone soil under different shear rates show typical strain softening characteristics. 2) The shear rate–internal friction angle curve showed a good logarithmic relationship. 3) The fundamental reason for the rapid sliding into the river after the instability of the main sliding zone of the Shanshucao landslide is the negative rate effect of the argillized interlayer sliding zone soil in the main sliding zone.

Investigation of Deep Shaft-Surrounding Rock Support Technology Based on a Post-Peak Strain-Softening Model of Rock Mass

To control the large deformation that occurs in deep shaft-surrounding rock, the post-peak strain-softening characteristics of deep jointed rock mass are discussed in detail. An equivalent post-peak strain-softening model of jointed rock mass is established based on continuum theory and the geological strength index surrounding rock grading system, and numerical simulations are performed using FLAC3D software. The convergence-constraint method is used to analyze the rock support structure interaction mechanism. A composiste support technique is proposed in combination with actual field breakage conditions. During the initial support stage, high-strength anchors are used to release the rock stress, and high-stiffness secondary support is provided by well rings and poured concrete. This support technology is applied in the accessory well of a coal mine in Niaoshan, Heilongjiang, China. The stability of the surrounding rock support structure is calculated and analyzed by comparing the ideal elastic-plastic model and equivalent jointed rock mass strain-softening model. The results show that a support structure designed based on the ideal elastic-plastic model cannot meet the stability requirements of the surrounding rock and that radial deformation of the surrounding rock reaches 300 mm. The support structure designed based on the equivalent joint strain-softening model has a convergence rate of surrounding rock deformation of less than 1 mm/d after 35 days of application. The surrounding rock deformation is finally controlled at 140 mm, indicating successful application of the support technology.

Mechanical properties of frozen ballast aggregates with different ice contents and temperatures

Ice is the main factor that influences the properties of frozen ballast layers. To investigate the mechanical properties of railway ballasted beds in cold regions under freezing conditions, ice–bonded ballast specimens were prepared, and uniaxial compression tests were performed in a negative temperature environment. At a low loading velocity (v = 0.01 mm/s), the effects of the ice content (2%–35%) and temperature (−5 to − 30 °C) were analysed. The experimental results showed that the stress–strain curves exhibited strain-softening characteristics at different ice contents and temperatures. With an increase in the ice content, the ductile characteristics of the frozen specimens improved. The failure mode changed from brittle failure to axial splitting failure. Moreover, the compressive strength increased exponentially, and the effective elastic modulus increased linearly. Temperature significantly influenced the strength and deformation behaviour of the frozen specimens. The lower the temperature, the higher the compressive strength and effective elastic modulus. The relationship between temperature and compressive strength could be expressed using a power function. Finally, an empirical formula for computing the compressive strength of the ice–bonded ballast was obtained, considering the combined effect of the ice content and temperature. This study revealed the mechanical properties and developed a model for predicting the strength of frozen ballast layers in cold regions.

Analysis of Layered Geogrids–Sand–Clay Reinforced Structures under Triaxial Compression by Discrete Element Method

Compared with the commonest geosynthetics-reinforced soil structures, layered geogrids–sand–clay reinforced (LGSCR) structures (School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China) can replace granular materials with clay as the primary backfill material. Up until now, the performance of LGSCR structures under triaxial compression has been unclear. In this paper, the discrete element method was used to simulate the triaxial compression test on the LGSCR samples. Based on the particle flow software PFC3D, three types of cluster particle-simulated sand and the reinforced joints of the geogrid were constructed by secondary development. The effects of the geogrid embedment in sand layers, the number and thickness of sand layers in relation to the deviatoric stress, and the axial strain and the shear strength index of the LGSCR samples were analyzed. The results showed that laying the sand layers in the samples can improve their post-peak strain-softening characteristics and increase their peak strengths under a high confining pressure. A geogrid embedment in sand layers can further enhance the ductility and peak strength of the samples, and in terms of the shear strength index, there is a 41.6% to 54.8% increase in the apparent cohesion of the samples.

Experimental Study on Failure Mechanical Properties of Two Kinds of Seafloor Massive Sulfides

Remarkable hydrostatic pressures have a significant effect on the failure mechanical properties of seafloor minerals, which also affects the selection and development of mining excavation tools. In this paper, a Brazilian splitting test and triaxial compression test were adopted to investigate the strength and deformation behavior of two kinds of seafloor massive sulfides (SMS) samples at a small-scale size. Based on the mineralogical characterization of the studied samples, the mechanical properties were preliminarily correlated with their internal structures and mineral compositions. Results indicate that there is a significant difference in the triaxial compression deformation properties between the two kinds of SMS samples and the geotechnical data are controlled by mineral type and composition, including porosity. In general, the triaxial compression process of the two kinds of samples included initial compaction, elastic stage, yield stage, failure stage and residual stage, and shows strain softening characteristics after the peak. With the increase in confining pressure, the strain-softening behavior of the white sample is mitigated and gradually changes into strain-hardening. The peak strength and peak strain of the two samples increased linearly with the increase in confining pressure within the confining pressure range of these tests, and the failure pattern of the specimens also changed from a typical brittle failure to a ductile failure. The results of this study provide data to support further understanding of different kinds of SMS, and are of great significance in the design of efficient SMS exploitation equipment.

Failure envelope of suction caisson anchors subjected to combined loadings in sand

This paper reports the behaviour of caisson anchors under vertical-horizontal (V-H) loadings in medium dense to dense sand. The three dimensional finite element (3D-FE) analyses are carried out using a modified Mohr-Coulomb (MMC) soil model to capture the stress dependent hardening – softening behaviour of sands. The results are validated against centrifuge test data prior to undertaking a detailed parametric study, exploring the relevant range of parameters in terms of caisson aspect ratio, padeye location, mooring angle at the padeye and sand relative density. It is found that the caisson anchor failure is governed by the sand relative density, mooring angle and the normalised padeye position. The padeye position not only affects the anchor capacity, but also influences the rotation angle of the caisson at failure. An optimal padeye position inducing minimal rotation at caisson failure is found to lie within the range of 0.6-0.7L, where L is the caisson length. To assess capacity under inclined loading, normalised failure envelopes are presented in the V-H space. A design framework is established to estimate the optimal padeye location and caisson capacity for sands with strain hardening – strain softening characteristics.

3D DEM simulation of initial anisotropy in dredger fill soft soil

The initial anisotropy has a significant effect on the mechanical properties of the soft soil. Based on the initial anisotropy of the particles, the mechanical characteristics are analysed from a microscopic view, and the micro-macro relationship of the soil is established. According to the particle morphology of soft soil, the discrete element method is used to construct the flaky particle clusters, and seven sets of samples with different initial deposition angles are established for consolidation and undrained triaxial simulation tests. The results show that the strength of the sample decreases first and then increases with the increase of the deposition angle. When the deposition angle is 0°, the flaky particles mostly appear in a nearly horizontal suspension, and the sample has the largest shear strength. The distribution of the contact force chain formed by the particles in the shearing process is also related to the deposition angle. Different deposition angles form displacement fields of different shapes. When the deposition angles are 45° and 60°, there are obvious deformation displacement bands. At the same time, the initial deposition angle affects the particle coordination number. The higher the sample strength corresponding to the lowest average coordination number of particles. The contact normal anisotropy coefficient is related to the strain hardening and strain softening characteristics in the shearing process. The increase in the contact normal anisotropy coefficient shows the characteristics of hardening, and the smaller the contact normal anisotropy coefficient shows the characteristics of softening.